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(B) Given $f(x) = e^x \sin x$. First derivative: $f'(x) = e^x \sin x + e^x \cos x = e^x(\sin x + \cos x)$. Second derivative: $f''(x) = e^x(\sin x + \

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$-8 e^x \cos x$

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(B) Given $f(x) = e^x \sin x$. First derivative: $f'(x) = e^x \sin x + e^x \cos x = e^x(\sin x + \cos x)$. Second derivative: $f''(x) = e^x(\sin x + \cos x) + e^x(\cos x - \sin x) = 2e^x \cos x$. Third derivative: $f'''(x) = 2e^x \cos x - 2e^x \sin x = 2e^x(\cos x - \sin x)$. Fourth derivative: $f^{(4)}(x) = 2e^x(\cos x - \sin x) + 2e^x(-\sin x - \cos x) = -4e^x \sin x$. Fifth derivative: $f^{(5)}(x) = -4e^x \sin x - 4e^x \cos x = -4e^x(\sin x + \cos x)$. Sixth derivative: $f^{(6)}(x) = -4e^x(\sin x + \cos x) - 4e^x(\cos x - \sin x) = -4e^x \sin x - 4e^x \cos x - 4e^x \cos x + 4e^x \sin x = -8e^x \cos x$.

$f(x) = e^x \sin x$,then $f^{(6)}(x)$ is equal to :

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